Mba0045
Operations Research
Unit 4
Unit 4
Simplex Method
Structure: 4.1 Introduction Objectives 4.2 Standard Form of LPP Fundamental theorem of LPP 4.3 Solution of LPP – Simplex Method Initial basic feasible solution of an LPP To solve an LPP in canonical form by simplex method 4.4 The Simplex Algorithm Steps 4.5 Penalty Cost Method or Big M-method 4.6 Two Phase Method 4.7 Solved Problems on Minimisation 4.8 Summary 4.9 Glossary 4.10 Terminal Questions 4.11 Answers 4.12 Case Study
4.1 Introduction
In the previous unit we dealt with graphical analysis of linear programming problems. We discussed some basic definitions, graphical methods to solve LPP, some exceptional cases, advantages, limitations, and important geometric properties of LPP. In this unit, we will deal with the simplex method, which focuses on solving an LPP of any enormity involving two or more decision variables. The simplex algorithm is an iterative procedure for finding the optimal solution to a linear programming problem. The objective function controls the development and evaluation of each feasible solution to the problem. If a feasible solution exists, it is located at a corner point of the feasible region determined by the constraints of the system. The simplex method simply selects the optimal solution amongst the set of feasible solutions of the problem. The efficiency of this algorithm is because it considers only those feasible solutions which are provided by the corner points, and that too not all of them.
Sikkim Manipal University Page No. 57
Operations Research
Unit 4
Objectives: After studying this unit, you should be able to: create a standard form of LPP from the given problem apply the simplex algorithm to the system of equations find solution using big M-technique explain the importance of the two phase method
4.2 Standard Form of LPP
The characteristics of the standard form of LPP are: All constraints are equations. The right-hand side element of
Unit 4
Unit 4
Simplex Method
Structure: 4.1 Introduction Objectives 4.2 Standard Form of LPP Fundamental theorem of LPP 4.3 Solution of LPP – Simplex Method Initial basic feasible solution of an LPP To solve an LPP in canonical form by simplex method 4.4 The Simplex Algorithm Steps 4.5 Penalty Cost Method or Big M-method 4.6 Two Phase Method 4.7 Solved Problems on Minimisation 4.8 Summary 4.9 Glossary 4.10 Terminal Questions 4.11 Answers 4.12 Case Study
4.1 Introduction
In the previous unit we dealt with graphical analysis of linear programming problems. We discussed some basic definitions, graphical methods to solve LPP, some exceptional cases, advantages, limitations, and important geometric properties of LPP. In this unit, we will deal with the simplex method, which focuses on solving an LPP of any enormity involving two or more decision variables. The simplex algorithm is an iterative procedure for finding the optimal solution to a linear programming problem. The objective function controls the development and evaluation of each feasible solution to the problem. If a feasible solution exists, it is located at a corner point of the feasible region determined by the constraints of the system. The simplex method simply selects the optimal solution amongst the set of feasible solutions of the problem. The efficiency of this algorithm is because it considers only those feasible solutions which are provided by the corner points, and that too not all of them.
Sikkim Manipal University Page No. 57
Operations Research
Unit 4
Objectives: After studying this unit, you should be able to: create a standard form of LPP from the given problem apply the simplex algorithm to the system of equations find solution using big M-technique explain the importance of the two phase method
4.2 Standard Form of LPP
The characteristics of the standard form of LPP are: All constraints are equations. The right-hand side element of
References: Kapoor V. K. (2005). Operations Research. Sultan Chand and Sons. Sharma J. K. (2006). Operations Research. Macmillan India Limited. Taha H. Operations Research. Prentice Hall. Kanti Swarup & Gupta P. K., & Hira D. S., & Manmohan (2004). Operation Research. Sultan Chand and Sons. E- Reference : The Design of Manufacturing Systems. http://www.springerlink.com Sikkim Manipal University Page No. 86